inf_sSup_eq_iSup_inf_sup_finset

∀ {α : Type u_2} [inst : CompleteLattice α] [IsCompactlyGenerated α] {a : α} {s : Set α},
  a ⊓ sSup s = ⨆ t, ⨆ (_ : ↑t ⊆ s), a ⊓ t.sup id

This property is equivalent to α being upper continuous.

Defined in: Mathlib.Order.CompactlyGenerated.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompleteLattice IsCompactlyGenerated

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